There have existed a number of drawbacks in previous imaging modalities, including medical imaging modalities such as magnetic resonance imaging (“MRI”) and computer tomography (“CT”) scanning.
MRI
MRI allows excellent visualization of anatomical structure and physiological function. However, it is a relatively slow imaging modality because the data, which are samples in k-space of the spatial Fourier transform of the object, are acquired sequentially in time. Therefore, numerous techniques have been proposed to reduce the amount of data required for accurate reconstruction, with the aim of enabling much higher clinical throughput, or accurately capturing time varying phenomena such as motion, changes in concentration, flow, etc., or avoiding artifacts due to such phenomena.
Compressed Sensing (CS) enables accurate image recovery from far fewer measurements than required by traditional Nyquist sampling. In order to do so, CS employs the sparsity or approximate sparsity of the underlying signal in some transform domain, dictionary, or basis, and a sampling pattern that is incoherent, in an appropriate sense, with the transform, dictionary, or basis. However, the reconstruction method is non-linear. Furthermore, compressed sensing MRI (“CSMRI”) reconstructions with fixed, non-adaptive sparsifying transforms typically suffer from many artifacts at high undersampling factors. One limitation of these CSMRI methods is their non-adaptivity to the measured data.
CT
Iterative reconstructions in x-ray CT attempt to recover high quality images from imperfect data, such as low-dose and/or incomplete or limited data, or to overcome artifacts due to the presence of dense objects, or imperfect models of the data acquisition process. To facilitate dose reduction, low-dose imaging methods typically incorporate detailed mathematical models of the image acquisition process, including models of the CT system, noise, and images. The mathematical models are combined into an unconstrained or constrained optimization problem, which is then solved using an optimization algorithm. The signal model takes the form of a function called a regularizer, which penalizes signals which do not fit the prescribed model, or constrains the solution to fit these models.
Choosing an appropriate regularizer, however, is not easy. Traditionally, the regularizer is based on a fixed, analytic transformation that causes images to become sparse or approximately sparse in some transform domain, dictionary, or basis. For example, total-variation regularization utilizes a finite-differencing matrix, and methods based on wavelet transformations have been successful. These signal models do not fully capture the relevant details of CT images. For example, total-variation regularization can result in images that have patchy artifacts as a result of the simplistic signal model. Reconstruction quality can be improved by incorporating better signal models.